document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=776314>Question 776314</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem with solutions so i can understand clearly: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287-5i%29%2F%283%2B6i%29 ALIGN=MIDDLE  ALT=\"%287-5i%29%2F%283%2B6i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #473496 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=473496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%287-5i%29%2F%283%2B6i%29+ ALIGN=MIDDLE  ALT=\"+%287-5i%29%2F%283%2B6i%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "What you are trying to do is to get this<BR>\n" );
document.write( "into the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+b%2Ai+ ALIGN=MIDDLE  ALT=\"+a+%2B+b%2Ai+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Multiply both top and bottom by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+-+6i+ ALIGN=MIDDLE  ALT=\"+3+-+6i+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is called the complex conjugate<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%287-5i%29%2F%283%2B6i%29+%29%2A+%28+%28+3+-+6i+%29+%2F+%28+3+-+6i+%29+%29+ ALIGN=MIDDLE  ALT=\"+%28+%287-5i%29%2F%283%2B6i%29+%29%2A+%28+%28+3+-+6i+%29+%2F+%28+3+-+6i+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the same as multiplying by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so you haven't changed anything<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Rewrite it as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%28+7+-+5i+%29%2A%28+3+-+6i+%29+%29+%2F+%28+%28+3+%2B+6i+%29%2A%28+3+-+6i+%29+%29+ ALIGN=MIDDLE  ALT=\"+%28+%28+7+-+5i+%29%2A%28+3+-+6i+%29+%29+%2F+%28+%28+3+%2B+6i+%29%2A%28+3+-+6i+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now multiply out the denominator as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+3+%2B+6i+%29%2A%28+3+-+6i+%29+=+9+%2B+18i+-+18i+-+36i%5E2+ ALIGN=MIDDLE  ALT=\"+%28+3+%2B+6i+%29%2A%28+3+-+6i+%29+=+9+%2B+18i+-+18i+-+36i%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the fact that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+i%5E2+=+-1+ ALIGN=MIDDLE  ALT=\"+i%5E2+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, I get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+3+%2B+6i+%29%2A%28+3+-+6i+%29+=+9+-+36%2A%28-1%29+ ALIGN=MIDDLE  ALT=\"+%28+3+%2B+6i+%29%2A%28+3+-+6i+%29+=+9+-+36%2A%28-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+3+%2B+6i+%29%2A%28+3+-+6i+%29+=+9+%2B+36+ ALIGN=MIDDLE  ALT=\"+%28+3+%2B+6i+%29%2A%28+3+-+6i+%29+=+9+%2B+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+3+%2B+6i+%29%2A%28+3+-+6i+%29+=+45+ ALIGN=MIDDLE  ALT=\"+%28+3+%2B+6i+%29%2A%28+3+-+6i+%29+=+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "Now my expression is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%28+7+-+5i+%29%2A%28+3+-+6i+%29+%29+%2F+45+ ALIGN=MIDDLE  ALT=\"+%28+%28+7+-+5i+%29%2A%28+3+-+6i+%29+%29+%2F+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now multiply out the numerator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+21+-+15i+-+42i+%2B+30i%5E2+ ALIGN=MIDDLE  ALT=\"+21+-+15i+-+42i+%2B+30i%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+21+-+57i+-+30+ ALIGN=MIDDLE  ALT=\"+21+-+57i+-+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-9+-+57i+ ALIGN=MIDDLE  ALT=\"+-9+-+57i+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Putting the numerator and denominator <BR>\n" );
document.write( "together, I get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+-9+-+57i+%29+%2F+45+ ALIGN=MIDDLE  ALT=\"+%28+-9+-+57i+%29+%2F+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-9%2F45+-+%2857%2F45%29%2Ai+ ALIGN=MIDDLE  ALT=\"+-9%2F45+-+%2857%2F45%29%2Ai+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1%2F5+-+%2857%2F45%29%2Ai+ ALIGN=MIDDLE  ALT=\"+-1%2F5+-+%2857%2F45%29%2Ai+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "I can check this result:<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%287-5i%29%2F%283%2B6i%29+=+%28+-9+-+57i+%29+%2F+45 ALIGN=MIDDLE  ALT=\"+%287-5i%29%2F%283%2B6i%29+=+%28+-9+-+57i+%29+%2F+45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+3+%2B+6i+%29%2A45+ ALIGN=MIDDLE  ALT=\"+%28+3+%2B+6i+%29%2A45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+7+-+5i+%29%2A45+=+%28+-9+-+57i+%29%2A%28+3+%2B+6i+%29+ ALIGN=MIDDLE  ALT=\"+%28+7+-+5i+%29%2A45+=+%28+-9+-+57i+%29%2A%28+3+%2B+6i+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+315+-+225i+=+-27+-+171i+-+54i+-+342i%5E2+ ALIGN=MIDDLE  ALT=\"+315+-+225i+=+-27+-+171i+-+54i+-+342i%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+315+-+225i+=+-27+-+171i+-+54i+%2B+342+ ALIGN=MIDDLE  ALT=\"+315+-+225i+=+-27+-+171i+-+54i+%2B+342+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+315+-+225i+=+315+-+225i++ ALIGN=MIDDLE  ALT=\"+315+-+225i+=+315+-+225i++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );